Model wormlike chain

For poly electrolyte solutions with added salt, prior experimental studies found that the intrinsic viscosity decreases with increasing salt concentration. This can be explained by the tertiary electroviscous effect. As more salts are added, the intrachain electrostatic repulsion is weakened by the stronger screening effect of small ions. As a result, the polyelectrolytes are more compact and flexible, leading to a smaller resistance to fluid flow and thus a lower viscosity. For a wormlike-chain model by incorporating the tertiary effect on the chain... 

Yamakawa and co-workers have formulated a discrete helical wormlike chain model that is mechanically equivalent to that described above for twisting and bending/79111 117) However, their approach to determining the dynamics is very different. They do not utilize the mean local cylindrical symmetry to factorize the terms in r(t) into products of correlation functions for twisting, bending, and internal motions, as in Eq. (4.24). Instead, they... 

Thermotropic liquid crystalline polymers, like polyesters containing mesogenic units on the main chain, may not be described by the wormlike chain model (cf. Sect. 1.2). The present article does not consider this type of polymers. 

Moha et al. (54) considered that polypeptides in helicogenic solvents can assume intact helices but that the resulting rods can be weakly bent, and proposed to represent such a flexible rod by a wormlike chain. It was shown that the nonlinear dependence of 1/2 on N as depicted in Fig. 21 can be fitted by a suitable choice of the two parameters characterizing the wormlike-chain model. However, the necessary value for the length per monomeric unit forces us to accept the conclusion that the helical conformation is not of the a-type but of the 310-type. This is at variance with the ample experimental evidence now available for many synthetic polypeptides. 

Investigations are presented concerning the relationship between the RIS and wormlike chain models. 

A comparison is presented between the behavior of unperturbed stars of finite size whose configurational statistics are evaluated by R1S theory and the Kratky-Porod wormlike chain model. Emphasis Is placed on the initial slopes of the characteristic ratio, C, or g when plotted as a function of the reciprocal of the number of bonds, n. 

A consideration of the molecular conformation using the wormlike chain model suggests that the curdlan molecule may contain helical portions but, as a whole, takes a random-coil conformation ( ) ... 

On the other hand, while the MW dependence of , diffusion, and sedimentation coefficients of these bottlebrushes were quantitatively described by the wormlike chain model, a significant disagreement between that of [q] and the theory was also reported [65-67]. This is an unsolved subject to be studied further. 

Persistence Length Evaluated using the Wormlike Chain Model ... 

Equilibrium rigidity is conventionally expressed in terms of the persistence length q based on the wormlike chain model (Fig. 37). Three methods for estimating q have been adopted 67). 

Wormlike chain model Wormlike touched beads model Wormlike cylinder model... 

Fig. 37a-c. Schematic representation of various wormlike chain models 67) d is the diameter of the touched bead and cylinder models... 

The qnD values of cellulose and its derivatives lie between 3 and 25 nm and are larger than those of typical vinyltype polymer ( 1 nm), but markedly smaller than those of typical stiff chain polymers, such as DNA (Table 14)67). Thus, the chains of cellulose and its derivatives can be considered as semi-flexible. It may be concluded that both the pearl-necklace chain and the wormlike chain models are adequately applicable to these polymers. 

In the diaryl-substituted polysilane, the global dimensions are approximated by a wormlike chain model with a persistence length of 100 A. Thus, for the highest molecular weight studied, LIq — 100, and the chain dimensions are similar to those of a flexible-model Kuhn chain with bond lengths IkOf —200 A, that is,... 

At a given force, the elasticity of covalent bonds of the amino acid backbone gives rise to a length increase. But thermal fluctuations act on the backbone, which on an average pulls the cantilever closer to the membrane, a phenomenon referred to as entropic elasticity of linear polymers. The wormlike chain model [50] describes the polymer as an elastic rod with bending stiffness submitted to thermal fluctuations that decrease the end-to-end distance of the rod. Alternatively, the freely jointed chain model calculates the... 

The relatively small region of allowable values of tp and j/ in polysaccharides linked between rings makes the wormlike chain model realistic for them. The polymer behaves as a random flight one over contour lengths S Lp, but as a stiff rod if S Lp. Persistence lengths can be fairly large 350 50 A for xanthan gum, 80-100 A for alginate or hyaluronate. ... 

The present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

When modeling a polymer that is rigid on the molecular scale of a few nanometers, it is natural to approximate it as an elastic rod that resists bending. This is the essence of the so-called wormlike chain model, which can be described by an elastic energy of the form... 

In other words, the local deformation energy is quadratic in the local curvature k s) when expanded to the lowest order in k. Conformations with Rlocal deformation energy greater than k T per unit length. Subjecting this model to thermal fluctuations results in the wormlike chain model. ... 

The simple picture afforded by the wormlike chain model is likely to break down under conditions of extreme deformation, as discussed in Section 9.13.2. The internal organization of dsDNA is likely to have instances where the chain is highly deformed, significantly beyond the range where linear elasticity theory is an adequate description. In addition, the potential for dsDNA to exhibit curvature-induced softening may promote... 

Figure 22.S GPC elugram of polymer 12 (Mw = 113 kg mop ) in THF PS calibration (solid line), universal calibration based on Mark-Houwink-Sakurada equation (dashed line), and universal calibration based on the wormlike chain model (dotted line). (Reproduced with permission from Ref [32].)...

Although the influence of the excluded volume is not taken into account, Picken s theory provides a satisfactory interpretation of the experimental results. The combination of a wormlike chain model and the Maier-Saupe approach has also been suggested by Jahnig [66], and is developed further by ten Bosch, Maissa and Sixou [67], as well as by Warner et al, [68]. 

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